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Aut-invariant Quasimorphisms on Groups by Fournier-Facio, Francesco; Wade, Richard D. is a scholarly article available to read on EtoBox.

What is Aut-invariant Quasimorphisms on Groups about?

For a large class of groups, we exhibit an infinite-dimensional space of homogeneous quasimorphisms that are invariant under the action of the automorphism group. This class includes non-elementary hyperbolic groups, infinitely-ended finitely generated groups, some relatively hyperbolic groups, and a class of graph products of groups that includes all right-angled Artin and Coxeter groups that are not virtually abelian. This was known for $F_2$ by a result of Brandenbursky and Marcinkowski, but is new even for free groups of higher rank, settling a question of Mikl\'os Ab\'ert. The case of graph products of finitely generated abelian groups settles a question of Michal Marcinkowski. As a consequence, we deduce that a variety of Aut-invariant norms on such groups are unbounded.

Author

Fournier-Facio, Francesco; Wade, Richard D.

Published

2022

Language

EN